Eric Cantor will be named as one of Jeb Bush’s three co-chairs in Virginia, marking a high-profile return to the national political scene for the former House majority leader who lost his seat in stunning fashion during last year’s primary election.

Former Virginia Secretary of Health Kay Cole James and former Virginia Lt. Gov. John Hager will round out the leadership team for Mr. Bush’s 2016 GOP presidential campaign in The Old Dominion.

Mr. Cantor, in a statement, called Mr. Bush “a true conservative leader with a long-term vision for this country and the practical know how to implement it.”

“After eight years of anemic growth and declining international relevance, America needs a President that can re-energize our nation and recapture our greatness — Jeb Bush is that man,” he said.

Mr. Cantor was the lone Jewish Republican in the House when he lost his seat in 7th congressional district in the 2014 GOP primary to Dave Brat, an economics professor at Randolph–Macon College. Tea partiers and grass-roots insurgent groups celebrated the upset, which rocked the political world.

Mr. Cantor, who had held the seat from 2001 to 2014, was later named a vice chairman of an investment firm.

The announcement could help Mr. Bush tap into the political network that Mr. Cantor built up over the years in Virginia, a key swing state in presidential elections, and around the nation.

Mr. Hager also has deep ties to the Virginia GOP, having served as the state party chairman, and to the Bush family. His youngest son, Henry, is married to Jenna Bush, one of former President George W. Bush’s twin daughters.

“Jeb Bush has the experience, with a great track record as Florida governor, a broad appeal and the strong Virginia values we need in a candidate for president,” Mr. Hager said in a statement.